Embodiments of the invention relate to a method and an apparatus for estimating deviations between free running transmitter clocks and a reference clock. In embodiments of the invention, the estimated deviations are used to virtually synchronize transmitters using the free-running transmitter clocks. In embodiments of the invention, deviation between a plurality of free-running transmitter clocks and the reference clock is estimated at a stationary receiver, the estimated deviations are sent to a movable object, wherein the movable object uses the estimated deviations and transmitter signals received from the plurality of free-running transmitter clocks to determine its position.
Synchronization is a pivotal element in any accurate positioning system based on time-of-arrival (TOA) or time-difference-of-arrival (TDOA) measurements. There are numerous publications on synchronization strategies for local navigation systems. Most of them build upon complex, fixed infrastructure or intelligent, expensive transmitters, [1] and [2].
A system comprising low-cost free-running transmitters which are virtually synchronized by means of a single, fixed reference station would be a solution. The reference station would then distribute the synchronization parameters wirelessly to the rovers. Obviously, such a solution means that any receiver in the system can adequately model the behavior of the different transmitter clocks. Most published clock error models are particularly suitable for long-term stable accurate clocks [3], [4], [5], [6].
All these models identify the types and determine the parameters of the noise components from plots of the Allan Variance or of the power spectral densities by a method called power-law noise identification which subdivides the plot into regions of different slopes. The parameters extracted from the Allan Variance can be used to set up a random process modeling the clock behavior. A drawback of this method is its limited applicability: some of the noise components are hard to model by a rational transfer function. Moreover, all the mentioned studies focus on the frequency modulate (FM) components: white FM, flicker FM, and random walk FM.
When short-term stability is of interest, phase modulated (PM) components: white and flicker PM noise, if present, are also taken into account. In this case, power-law noise identification by simply reading the noise parameters from the Allan Variance leads to non rational transfer functions.
A different approach to noise identification is based on the autocorrelation function of the phase noise as presented in [7], applied there to any type of noise.
US 2006/029009 A1 discloses a system of measuring the range between nodes in a wireless communications network with one-way data transfer, where each node periodically transmits a message that contains information regarding neighboring nodes from which any prior messages have been received by the transmitting node. A node receives the messages transmitted from neighboring nodes in the network, and records the times of arrival of the received messages. The node receiving those messages can thus determine the respective distances between itself and the neighboring nodes based on the respective time of arrivals of the received messages and the respective information included in the respective messages.
Mouly M; Dornstetter J-L: “The Pseudo-Synchronisation, a Costless Feature to Obtain the Gains of a Synchronised Cellular Network” MRC Mobile Radio Conference, XX, XX, 1 Nov. 1991 (Nov. 1, 1991), pages 51-55, XP000391318, disclose a pseudo-synchronization scheme for a cellular radio telephone system. An accurate knowledge of phase differences between the time basis of different base stations is maintained and each base station stores the time difference with its neighbors. Once known, the time differences are sent to the entity needing them at the moment they need them, for instance to a mobile station when ordered to another cell.
Carpenter R; Lee T: “A stable clock error model using coupled firs and second-order gauss-markov processes” Advances in the Astronautical Sciences—Space Flight Mechanics 2008—Advances in the Astronautical Sciences, Proceedings of the AAS/AIAA Space Flight Mechanics Meeting 2008 Univelt Inc. US, 31 Dec. 2008 (Dec. 31, 2008), pages 1-13, XP002545930, teaches a stable clock error model using coupled first—and second—order gauss-markov processes.
Nicola Altan; Erwin P Rathgeb Ed—David Coudert; David Simplot-RYL, Ivan Stojomenovic: “Opportunistic Clock Synchronization in a Beacon Enabled Wireless Sensor Network” 10 Sep. 2008 (Sep. 10, 2008), AD-HOC, Mobile and Wireless Networks; 20080910 Springer Berlin Heidelberg, Berlin, Heidelberg, page(s) 15-28, XP019102619 ISBN: 9783540852087, teach a clock synchronization in a beacon enabled wireless sensor network consisting of a large number of tiny inexpensive sensor nodes. A time synchronization mechanism based on the usage of a Kalman Filter on a smoothed sequence of measured beacon intervals is proposed. A global clock synchronization is introduced.